Question

what is the surface area of the following cone? a 60π cm² b 72π cm² c 96π cm² d 132π cm²

Explanation:

Step1: Find the radius

The diameter is 12 cm, so the radius $r=\frac{12}{2}=6$ cm.

Step2: Calculate the slant - height $l$

Using the Pythagorean theorem $l = \sqrt{h^{2}+r^{2}}$, where $h = 8$ cm and $r = 6$ cm. So $l=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10$ cm.

Step3: Calculate the surface area of the cone

The surface area of a cone $S=\pi r(r + l)$. Substitute $r = 6$ cm and $l = 10$ cm into the formula: $S=\pi\times6\times(6 + 10)=\pi\times6\times16=96\pi$ $cm^{2}$.

Answer:

C. $96\pi$ $cm^{2}$